Afirst number plus twice a second number is 10. twice the first number plus the second totals 32. find the numbers.

First num= x ,second num=y

X+2y=10
2x+y=32

Use equation 1 in equation 2
X=10-2y

2(10-2y)+y=32
20-4y+y=32
-3y = 12
Y= -4

X+2(-4)=10
X=10+8
X=18

Firstnum = 18 , second num= -4

Let first number be x
And the second number be y
Then, x + 2y = 10.
⇒ x = 10- 2y(1)

Also, 2x + y = 32 ...(2)

From, equation (1) & (2) we get, 
2(10-2y) + y = 32

or 20 - 4y + y  =32
or 20 - 32 = 3y 
or y = 4

Therefore, x = 10- 2y
or x = 10-2*4
or x = 10 - 8
or x = 2
Therefore, the two numbers are 2 & 4